Forecasting a live, real-world flow and learning from every measurement as it arrives.
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Method · Results · Experiment ledger · Reproducing
Most forecasting benchmarks hand a model one window, check its answer, and move on. Track 2 of the RealPDE Competition works more like deployment. The model watches a real, measured flow past an airfoil as one long, ordered stream:
observe 20 frames ─▶ forecast the next 20 ─▶ the truth is revealed ─▶ adapt ─▶ forecast again ─▶ …
Each revealed window becomes the next measured input; predictions are not fed back as future inputs. The challenge is to correct persistent bias and fluctuation errors as the measured flow evolves. The rules are strict: a forecast may only learn from targets that have already been revealed, and everything the model adapts has to be wiped clean when a new trajectory begins.
An illustration I generated, not competition data: the wake of a NACA4418 airfoil from a small lattice-Boltzmann simulation (left), and the same flow degraded the way PIV measurements are (right). How it was made
That's the catch. The model starts out trained on clean simulations like the left panel, but the stream it has to keep up with is measured, like the right: affected by measurement noise and differences from the simulated flow. (The competition website shows the real side-by-side.)
Scored on: field accuracy (Rel-L2), turbulent kinetic energy (TKE), the mean wake profile (MVPE), speed, and the quality of its uncertainty bounds (SPS).
My best submission, E033, doesn't retrain anything during the stream. Instead of running gradient updates on the fly, which I tried and found slow for very little gain, it keeps a few cheap running statistics and uses them to nudge each new forecast.
1 · Split the forecast into "average" and "wiggle." I started from the organizers' simulation-pretrained Fourier neural operator (FNO) and gave it two output heads: one for the temporal-mean flow and one for the zero-mean fluctuations around it. Their sum is the forecast. The simulation checkpoint's final layer is copied into both heads, preserving the original mapping up to floating-point roundoff. I check loaded parameters tensor by tensor and test forward equivalence within numerical tolerance.
2 · Fine-tune on real flow. 1800 updates on all 81 valid real trajectories, sampling each trajectory equally so long ones don't dominate.
3 · Adapt while streaming. Each time a target is revealed:
| Running statistic | What it corrects |
|---|---|
| Mean-bias EMA (decay 0.90): how far off my last forecast's average was | Systematic drift in the mean flow |
| Per-pixel variance EMA (decay 0.90): how much the real flow is fluctuating | Fluctuations that are too weak or too strong. They get rescaled by a bounded, smoothed ratio. |
4 · Say how unsure it is. Calibrated symmetric intervals
pred ± half_width, where the physical-space half-width is
0.020·abs(pred) + 0.140·σ_global and σ_global = 0.0563870259 is the
organizer's fixed scale, not a learned per-pixel uncertainty. Bounds are then
returned in normalized space, with finite-value guards.
5 · Reset at every trajectory boundary. No state, cache or statistic leaks from one trajectory to the next.
The details, configs and caveats are in METHOD.md.
Every point below is an official development-leaderboard score I recorded from Codabench—not a final private-test ranking or a fresh reproduction. Getting there took 30-plus numbered experiments over the competition.
xychart-beta
title "Official development-leaderboard score (final_score)"
x-axis [E007, E016, E022, E029, E033]
y-axis "final_score" 75 --> 78
line [75.42, 75.50, 76.50, 76.76, 77.62]
| Submission | What changed | Score |
|---|---|---|
| E007 | First validated streaming package | 75.42 |
| E016 | Same FNO recipe, refit on all real trajectories | 75.50 |
| E022 | Dual-head (mean + fluctuation) FNO with streaming mean-bias correction | 76.50 |
| E029 | Per-pixel streaming variance adaptation (TKE +6.6 over E022) | 76.76 |
| E033 | Verified simulation initialization + balanced sampling + longer training | 77.62 |
E033's full score breakdown
| What was measured | Metric | Score |
|---|---|---|
| Flow-field accuracy | Rel-L2 | 93.614317 |
| Turbulent energy | TKE | 77.141376 |
| Mean wake profile | MVPE | 93.391126 |
| Inference speed | Time | 88.185671 |
| Uncertainty quality | SPS | 32.109079 |
| Overall | final_score | 77.615784 |
E033 improved all four quality metrics over E029, while Time dipped slightly. It combined several changes, so one server comparison can't say which one mattered most. These are the development-leaderboard results I recorded from Codabench, not a final private-test ranking or a fresh reproduction. Full results and caveats →
- 🐢 Gradient-based test-time training. Updating the whole model, or just its last layer, on each revealed window cost runtime and bought almost nothing. Simple running statistics did far more.
- 🕵️ The initialization that wasn't. A checkpoint-loading bug left E021, the model behind E022/E029, at random weights instead of loading its configured E004 real-finetuned checkpoint. After fixing the loader, the separate E031 study showed that official simulation initialization improved every quality metric in all four fold/seed checks. The E021 record is corrected; E020's earlier history remains qualified. Initialization is now verified from loaded tensors, not trusted from a config label.
- 🌀 Mixing simulation into fine-tuning. Training jointly on simulated and real data, without aligning them first, collapsed the turbulent energy score.
- 📉 Fancier uncertainty and feedback. Learned variance heads, coverage feedback, residual feedback and input blending either failed their gates or lost to the plain variance-EMA approach.
- ☁️ Not every failure is yours. One submission failed because the platform couldn't fetch the organizers' ingestion bundle, before my code even ran.
Every experiment, the dead ends included, is in the
experiment ledger and the per-experiment notes in
docs/.
| If you want to… | Go to |
|---|---|
| Understand the approach | METHOD.md |
| See the numbers and their caveats | RESULTS.md · E033 notes |
| Follow the whole research story | LEDGER.md · literature notes · task reference |
| Read the code | src/realpde_t2/ · scripts/ · configs/ · submission/ |
| Rebuild the environment | REPRODUCING.md · EXTERNAL_DEPENDENCIES.md · environment-locks/ |
This is a research archive, not a pretrained model you can download and run.
- ✅ Included: my source code, configurations, contract tests, per-experiment result notes, and pinned dependency snapshots for reconstructing the environments.
- ❌ Not included: competition data, trained checkpoints, generated submission archives, installed environments, or the organizer starter kit. Data, learned weights and generated submissions were deleted during cleanup after the development phase. The organizer kit was deliberately excluded from this public export; obtain it separately under its terms.
⚠️ Not re-run: reproducing E033 means reacquiring the data and retraining. I haven't done a fresh end-to-end run since the cleanup. See REPRODUCING.md.
You can check the archive right away. No GPU, data or packages needed:
python3 -B scripts/check_archive.py
python3 -B scripts/publication_audit.pyThese check source integrity, license headers and release hygiene, not
model quality. Clone as RealPDE_T2 if you want paths to match the original
workspace layout.
Sibling project:
realpde-track1covers Track 1, where a simulation-trained model has to transfer to real measurements.
Built by Pranay Vandanapu, with AI coding assistance (details). Huge thanks to the RealPDE organizers and the RealPDEBench team for the dataset, the baselines and a genuinely interesting problem. The flow animation is my own illustration, made with a small script (how it was made).
My original code is MIT-licensed, but not the whole repository. Five files adapt FNO code from RealPDEBench and are CC BY-NC 4.0 (non-commercial). They're listed in LICENSING.md and carry their own headers. See also THIRD_PARTY_NOTICES.md · PUBLICATION_AUDIT.md.